Soak bamboo skewers in water for 30 minutes. Toss cubed chicken with 1 tbsp olive oil, salt, and pepper. Skewer chicken and place on baking sheet.
In a food processor, combine all pesto ingredients, except for the olive oil. Pulse a few times, then drizzle the olive oil down the feeding tube as you pulse. Add enough oil to create a pesto consistency. Set aside.
Broil chicken on second-to-highest rack for 3 minutes on each side, or until cooked through. Transfer to serving plate and top with pesto (or serve on the side as a dipping sauce.)